Lecture 16| Improper Integral using rectangular contour integration| Example 1| Theta Classes

In this lecture we are going to introduce another type of contour which is being used to solve improper integral using the method of contour integration. So first we see that when integrand involves hyperbolic or periodic functions then we will use rectangular contour . After that we will find the poles of the function and locate them in z plane and then we will form a rectangle in such a way that only one pole lies within that and then we apply Cauchy Residue theorem. After that we will break our contour into four parts and solve each integral along particular path and see their value as R tends to infinity. And then after some calculation we will get our result. In case if any student finds any difficulty in understanding this lecture do mention it in comment section. Keep connected with ‪@thetaclasses‬ to study various topics of higher mathematics. Thank You.